Algebraic dimension of twistor spaces

1988 ◽  
Vol 282 (4) ◽  
pp. 621-627 ◽  
Author(s):  
Y. Sun Poon
Keyword(s):  
Twistor Spaces ◽  
Algebraic Dimension

scholarly journals Geometry of some twistor spaces of algebraic dimension one

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Nobuhiro Honda
Keyword(s):  
Twistor Space ◽  
Projective Planes ◽  
Canonical System ◽  
K3 Surface ◽  
Twistor Spaces ◽  
Algebraic Dimension ◽  
General Fiber ◽  
Algebraic Reduction ◽  
Dimension One ◽  
Complex Projective

AbstractIt is shown that there exists a twistor space on the n-fold connected sum of complex projective planes nCP2, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over nCP2 for any n ≥ 5, while the latter kind of example is constructed over 5CP2. Both of these seem to be the first such example on nCP2. The algebraic reduction in these examples is induced by the anti-canonical system of the twistor spaces. It is also shown that the former kind of twistor spaces contain a pair of non-normal Hopf surfaces.

scholarly journals Generalized almost even-Clifford manifolds and their twistor spaces

2021 ◽  
Vol 8 (1) ◽  
pp. 96-124
Author(s):  
Luis Fernando Hernández-Moguel ◽  
Rafael Herrera
Keyword(s):  
Twistor Space ◽  
Complex Structure ◽  
Twistor Spaces ◽  
Recent Interest ◽  
Generalized Complex Structure ◽  
Generalized Complex ◽  
Space Construction ◽  
Clifford Structures

Abstract Motivated by the recent interest in even-Clifford structures and in generalized complex and quaternionic geometries, we introduce the notion of generalized almost even-Clifford structure. We generalize the Arizmendi-Hadfield twistor space construction on even-Clifford manifolds to this setting and show that such a twistor space admits a generalized complex structure under certain conditions.

scholarly journals Schottky groups acting on homogeneous rational manifolds

2019 ◽  
Vol 2019 (753) ◽  
pp. 23-56 ◽  
Author(s):  
Christian Miebach ◽  
Karl Oeljeklaus
Keyword(s):  
Deformation Theory ◽  
Group Actions ◽  
Picard Group ◽  
Schottky Group ◽  
Fundamental Groups ◽  
Complex Manifolds ◽  
Schottky Groups ◽  
Algebraic Dimension ◽  
Geometric Invariants ◽  
Compact Complex Manifolds

AbstractWe systematically study Schottky group actions on homogeneous rational manifolds and find two new families besides those given by Nori’s well-known construction. This yields new examples of non-Kähler compact complex manifolds having free fundamental groups. We then investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to Lárusson and to Seade and Verjovsky. As a byproduct, we see that the Schottky construction allows to recover examples of equivariant compactifications of {{\rm{SL}}(2,\mathbb{C})/\Gamma} for Γ a discrete free loxodromic subgroup of {{\rm{SL}}(2,\mathbb{C})}, previously obtained by A. Guillot.

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